3.2linear_regression.py

import random
import torch

def synthetic_data(w, b, num_examples):
    """
    """
    X = torch.normal(0, 1, (num_examples, len(w)))
    y = torch.matmul(X, w) + b
    y += torch.normal(0, 0.01, y.shape)
    return X, y.reshape((-1, 1))


true_w = torch.tensor([2, -3.4])
true_b = 4.2
print(true_w)
features, labels = synthetic_data(true_w, true_b, 1000)
print('features:', features[0],'\nlabel:', labels[0])


def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    random.shuffle(indices)
    for i in range(0, num_examples, batch_size):
        batch_indices = torch.tensor(
            indices[1: min(i + batch_size, num_examples)])
        yield features[batch_indices], labels[batch_indices]

batch_size = 10
for X, y in data_iter(batch_size, features, labels):
    print(X, '\n', y)
    break


"""
初始化模型参数
从均值为0，标准差为0.01的正态分布中采样随机数来初始化权重
将偏置初始化为0
"""
w = torch.normal(0, 0.01, size = (2,1), requires_grad = True)
b = torch.zeros(1, requires_grad = True)
print(w)
print(b)


"""
定义模型
"""
def linreg(X, w, b):
    return torch.matmul(X, w) + b


"""定义损失函数"""
def squared_loss(y_hat, y):
    return (y_hat - y.reshape(y_hat.shape))**2 / 2


"""定义优化算法"""
def sgd(params, lr, batch_size):
    """小批量随机梯度下降"""
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad / batch_size
            param.grad.zero_()

"""训练"""
lr = 0.03
num_epochs = 100
net = linreg
loss = squared_loss
for epoch in range(num_epochs):
    for X, y in data_iter(batch_size, features, labels):
        l = loss(net(X, w, b), y)
        l.sum().backward()
        sgd([w, b], lr, batch_size)
    with torch.no_grad():
        train_l = loss(net(features, w, b), labels)
        print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')

print(f'w的估计误差: {true_w - w.reshape(true_w.shape)}')
print(f'b的估计误差: {true_b - b}')